How to solve using perfect square x^2-4x-32=0

1 answer:

5 0

$Perfect\ square:(a-b)^2=a^2-2ab+b^2\\\\x^2-4x-32=0\ \ \ \ |add\ 32\ to\ both\ sides\\\\x^2-4x=32\\\\x^2-2x\cdot2=32\ \ \ \ |add\ 2^2\ to\ both\ sides\\\\x^2-2x\cdot2+2^2=32+2^2\\\\(x-2)^2=32+4\\\\(x-2)^2=36\iff x-2=-\sqrt{36}\ or\ x-2=\sqrt{36}\\\\x-2=-6\ or\ x-2=6\ \ \ \ |add\ 2\ to\ both\ sides\\\\\boxed{x=-4\ or\ x=8}$

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Luda [366]

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3 years ago

A car company claims that its new car, the GoFast2000, has a gas mileage of 35 miles per gallon ( mpg ). A consumer group suspec

I am Lyosha [343]

Answer:

H₀: μ = 35 mpg vs. Hₐ: μ < 35 mpg.

A t-test statistic should be used.

The company's claim is correct.

The true mean gas mileage of the new cars is 35 mpg.

Step-by-step explanation:

The consumer group can perform a test for single mean to determine whether the is less than 35 mpg or not.

The hypothesis can be defined as follows:

H₀: The true mean gas mileage of the new cars is 35 mpg, i.e. μ = 35 mpg.

Hₐ: The true mean gas mileage of the new cars is less than 35 mpg, i.e. μ < 35 mpg.

The information provided is:

n = 50

$\bar x$ = 34.8 mpg

As there is no information abut the population standard deviation then we would have to compute the sample standard deviation to estimate the value of σ.

Since the sample standard deviation will be used, a t test statistic would have to be computed.

The test statistic is given by:

$t=\frac{\bar x-\mu}{s/\sqrt{n}}$